The stability of bcc-Fe at high pressures and temperatures with respect to tetragonal strain

Abstract

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Lattice instabilities in metallic elements

“…Craievich et al (1994) obtained C 0 > 0 for the fcc structure and C 0 < 0 for the bcc structure of Mn (NM), Tc, and Re. This is consistent with C 0 and phonon spectrum (Persson, Ekman, and Grimvall, 1999) calculations for Re at P ¼ 0, and under pressure (Verma et al, 2003). Further, C 0 < 0 in bcc Mn (AF) Ma (2000a, 2000b).…”

“…However, bcc Fe may be stabilized at the conditions of the Earth's inner core (Belonoshko, Ahuja, and Johansson, 2003). For other works on Fe under pressure, see Vočadlo et al (2008) and references therein. An overview of ab initio calculations of elastic properties from the electronic ground state to the stability limit, with an application to bcc Fe, is given by .…”

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

“…For example, locating a path in the T /V space having no instability can avoid the former challenge. For the latter, the vibrationally unstable crystal can be (at least for some cases) deformed to another stable polymorph (e.g., using Bain path between fcc and bcc structures 61,62 ); alternatively, as discussed above, constraints can be introduced to stabilize the crystal until reaching a condition where it is inherently stable 44,54 . The TI formula for the classical anharmonic contribution is…”

“…Hence, even more rigorous methods are needed to evaluate the FE of crystals as robustly as possible, if only to provide a basis for evaluating methods based on an effective harmonic model. Along these lines, AIMD calculations have been attempted for iron at extreme conditions [40][41][42][43][44][45] , but these efforts have had to use approximations of their own, in the DFT treatment and/or the FE computational method, trading off accuracy to gain useful precision in the result. Due to these challenges associated with ab initio-based approaches, classical force-fields and/or theories are often adopted to get an estimate of the FE.…”

Dynamic X-ray diffraction observation of shocked solid iron up to 170 GPa

“…On this point, contradictory results have been published concerning the crystallographic structure of iron under Earth's inner core conditions (360 GPa and ∼6,000 K). Recent static compression on iron (11) and iron alloys (12) has highlighted the stability of hexagonal-close-packed (hcp) structure under extreme conditions, whereas previous studies investigated the potential stabilization of double hcp (dhcp) or body-centered cubic (bcc) structures under high pressure and temperature (13)(14)(15)(16)(17). However, having an hcp structure under Earth's inner core conditions is mandatory to explain its anisotropic structure observed by seismology (18,19).…”